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1 year ago

3. Elena had 12 hours working at home daily as a full-time wife and mother. She

Mathematics

2 answers:

KonstantinChe [14]1 year ago

8 0

Answer:

Elena spends 1.5 hours washing clothes.

Step-by-step explanation:

12.5 / 100 = 0.125

0.125 x 12 = 1.5

gizmo_the_mogwai [7]1 year ago

3 0

The answer is 8 hours

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Please help me out with this question

sleet_krkn [62]

Answer:

0.31%

Step-by-step explanation:

Just look at the graph my man

5 0

2 years ago

Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

2 years ago

If the farmer has 250 feet of fencing to create a rectangular pen, define a function f that expresses the area of the field (mea

hoa [83]

Answer:

Maximum area possible

f(max) = 3906,25 ft²

Dimensions:

a = 62,5 ft

w = 62,5 ft

Step-by-step explanation:

Perimeter of the rectangular fencing P = 250 feet

And sides of the rectangle a and w (width of rectangle)

Then

A = a*w

2a + 2w = 250 ⇒ a = (250 -2w)/ 2 ⇒ a = 125 - w

f(w) = (125 - w ) *w f(w) = 125w - w²

Taking derivatives both sides of the equation

f´(w) = 125 - 2w f´(w) = 0 125 - 2w = 0

w = 125/2

w = 62,5 ft ⇒ a = 125 - 62,5

a = 62,5 ft

f(max) = ( 62,5)²

f(max) = 3906,25 ft²

8 0

2 years ago

If dy/dx = x(y-1), find the equation of the tangent line at x=-2 with f(-2)=3

Lapatulllka [165]

Answer:

The equation of the tangent line passing through the point (-2,3) is

4 x + y +5 =0

Step-by-step explanation:

Step(i):-

Given that the slope of the tangent

$m = \frac{dy}{dx} = x(y-1)$

m = -2( 3-1) = -4

Given point x = -2

y = f(-2) =3

∴The given point ( x₁ , y₁) = ( -2 ,3)

Step(ii):-

The equation of the tangent line passing through the point (-2,3)

$y - y_{1} = m(x-x_{1} )$

$y -3 = -4(x-(-2))$

y -3 = -4( x+2)

y-3 = -4x -8

4x + y -3+8=0

4x +y +5=0

Step(iii):-

The equation of the tangent line passing through the point (-2,3) is

4 x + y +5 =0

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2 years ago

Find the length of each model. Then find the scale factor. (Pictures attached #3/#4)

max2010maxim [7]

12 cm for the first one and 11.6 for the second.

Unrelated to the question, that house around number 3 gives me nostalgia of elementary school :)

6 0

2 years ago